NCERT Solutions for Chapter: Heron's Formula, Exercise 4: Exercise

How much paper of each shade is needed to make a kite given in the figure, in which $\mathrm{ABCD}$ is square with diagonal $44 \mathrm{cm}$?

The perimeter of a triangle is $50 \mathrm{cm}$. One side of a triangle is $4 \mathrm{cm}$ longer than the smaller side and the third side is $6 \mathrm{cm}$ less than twice the smaller side. Find the area of the triangle.

The area of trapezium is $475 {\mathrm{cm}}^2$ and height is $19 \mathrm{cm}$. Find the lengths of its two parallel sides if one side is $4 \mathrm{cm}$ greater than the other.

A rectangular plot is given for constructing a house having a measurement of $40 \mathrm{m}$ length and $15 \mathrm{m}$ in the front. According to the laws, a minimum of $3 \mathrm{m}$ wide space should be left in the front and back each and $2 \mathrm{m}$ wide space on each of other sides. If the largest area where the house can be constructed is $k {\mathrm{m}}^2$, find the value of $k$.

A field is in the shape of a trapezium having parallel sides $90 \mathrm{m}$ and $30 \mathrm{m}$. These sides meet the third side at right angles. The length of the fourth side is $100 \mathrm{m}$ . It $₹4$ costs to plough $1 {\mathrm{m}}^2$ of the field. If the total cost of ploughing the field is $₹k$, then find the value of $k$.

In figure, $△\mathrm{ABC}$ has sides $\mathrm{AB}=7.5 \mathrm{cm}, \mathrm{AC}=6.5 \mathrm{cm} \mathrm{and} \mathrm{BC}=7 \mathrm{cm}$. On base $\mathrm{BC}$ a parallelogram $\mathrm{DBCE}$ of same area as that of $△\mathrm{ABC}$ is constructed. Find the height $\mathrm{DF}$ of the parallelogram.

The dimensions of a rectangle $\mathrm{ABCD}$ are $51 \mathrm{cm} \times 25 \mathrm{cm}$. A trapezium $\mathrm{PQCD}$ with its parallel sides $\mathrm{QC} \mathrm{and} \mathrm{PD}$ in the ratio $9:8$, is cut off from the rectangle as shown in the figure. If the area of the trapezium $\mathrm{PQCD}$ is $\frac{5}{6}\mathrm{th}$ part of the area of the rectangle. Find the lengths $\mathrm{QC}$ and $\mathrm{PD}$.

A design is made on a rectangular tile of dimensions $50 \mathrm{cm}\times 70 \mathrm{cm}$ as shown in figure. The design shows $8$ triangles, each of sides $26 \mathrm{cm},17 \mathrm{cm} \mathrm{and} 25 \mathrm{cm}$. Find the total area of the design and the remaining area of the tile.